Transformed Technique for Applying the Generalized Extreme Value Distribution to Block Minima

This study proposes a novel approach for analyzing block minima data within the Generalized Extreme Value Distribution (GEVD) framework by incorporating the Negative Power Transformation (NPT). The NPT method, which includes a hyper-parameter to adjust data bounds (effectively reducing to the Reciprocal Transformation (RT) when the hyper-parameter is 1), aims to improve the accuracy and robustness of long-term return level (RL) estimations. Traditional transformation methods often exhibit limitations in accurately predicting RLs for extended return periods. Through extensive Monte Carlo simulations, we demonstrate that the NPT-GEVD method outperforms conventional approaches in terms of bias, standard error (SE), and root mean square error (RMSE) for return periods of 25, 50, and 100 years. Notably, the NPT-GEVD consistently provides reliable RL estimates across various parameterizations and sample sizes, particularly when using L-moments for estimation with smaller datasets. The efficacy of the NPT-GEVD method is further validated through its application to inter-arrival time (IAT) rainfall data from South Korea. The analysis revealed that RLs for detecting the time to exceed hourly cumulative rainfall thresholds of 60 mm, 90 mm, and 110 mm varied significantly across locations, ranging from 30 minutes to over 4 hours. This research underscores the significance of advanced transformation techniques in enhancing the accuracy and reliability of environmental risk assessments. The NPT-GEVD method offers valuable insights for improving flood prediction and mitigation strategies in the face of climate change.